Reduction formula for point group S10

Your representation

E C5 (C5)2 (C5)3 (C5)4 i (S10)7 (S10)9 S10 (S10)3
36 3.2361 -1.2361 -1.2361 3.2361 0 -0.0000 0.0000 0.0000 -0.0000

can be reduced to

Ag E1g E2g Au E1u E2u
4 4 3 4 4 3

Substraction of translational and rotational contributions results in

Ag E1g E2g Au E1u E2u
3 3 3 3 3 3



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag E1g E2g Au E1u E2u
Infrared - - - + + -
Raman + + + - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 30 30 3
quadratic 900 465 48
cubic 27000 4960 496
quartic 810000 40920 4104
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field Ag E1g E2g Au E1u E2u
linear 3 3 3 3 3 3
quadratic 48 48 48 45 45 45
cubic 496 496 496 496 496 496
quartic 4104 4104 4104 4080 4080 4080

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group S10 Jacobs University Bremen